A decision feedback equalizer (DFE) is usually applied in the equalization of a modern communication system, such as the Advanced Television Systems Committee, ATSC). Generally, digital 8-level vestigial sideband (8-VSB) is utilized as the modulation method.
FIG. 1 shows a schematic diagram of data frames according to the conventional ATSC standard for high definition television (HDTV) system. Each data frame 100 includes two fields. Each field has one field sync segment (FIELD_SYNC #1 or #2) 102 and 313 data segments (DATA) 104. Each segment begins with four binary-level symbols (SEGMENT_SYNC) 106 having a regular pattern of {+5, −5, −5, +5}. In a data segment 104, the number of eight hundred twenty eight symbols 108 are data symbols resulting from forward error correction (FEC) coding and having values randomly in {+−1, +−3, +−5, +−7}. In the field sync segment 102, the 828 symbols 108 mostly include binary {+5, −5} pseudo random (PN) sequences. These PN sequences are used to train the coefficients of the equalizer such that the equalizer can compensate for the intersymbol interference (ISI) caused by the multi-path propagation of the signal.
Typically, the conventional equalizer operates based on two modes, including a training mode and an error tracking mode. The equalizer is represented by the following formula:
      x    ⁡          [      k      ]        =                    ∑                  i          =          0                                      N            b                    -          1                    ⁢                                    a            i                    ⁡                      [            k            ]                          ⁢                  y          ⁡                      [                          k              -              i                        ]                                -                  ∑                  j          =          1                          N          a                    ⁢                                    b            j                    ⁡                      [            k            ]                          ⁢                              x            ^                    ⁡                      [                          k              -              j                        ]                              
where “ai” is the feed-forward filter coefficients, “y” is the input signal, “bj” is the feedback filter coefficients, “x” is the equalizer output signal, “Na” is the range of “i”, “Nb” is the range of “j”, and {circumflex over (x)} is decision device output.
In the training mode, the feed-forward filter coefficient “ai” and the feedback filter coefficient “bj” are represented by the following expressions:ai[k+1]=ai[k]−μeD[k]y[k−i]bj[k+1]=bj[k]+μeD[k]{circumflex over (x)}[k−j]
where “eD” is called the decision-directed error and represented by the following expression:eD[k]=x[k]−{circumflex over (x)}[k]
In the error tracking mode using stop-and-go (SAG) algorithm, the feed-forward filter coefficient “ai” and the feedback filter coefficient “bj” are represented by the following expressions:ai[k+1]=ai[k]−μf[k]eD[k]y[k−i]bj[k+1]=bj[k]+μf[k]eD[k]{circumflex over (x)}[k−j]f[k]=1 if sgn{eD[k]}=sgn{es[k]} and f[k]=0 otherwise
where “es” is called the Sato error and represented by the following expression:es[k]=x[k]−γsgn{x[k]} and γ=E[|xc[k]|2]/E[|xc[k]|]
where “γ” is a constant scalar, sgn [ ] is the signum function, “E{ }” stands for expectation, and “xc[k]” is the transmitted symbol.
However, DFE-based receivers have an inherent potential to turn single error to burst errors, the so-called error propagation. Moreover, the equalizer usually needs millions of symbols to be converged.
Consequentially, there is a need to develop a novel decision feedback equalizer (DFE) to solve the aforementioned problems.